1. 2
Chapter
Chapter 2
Equations, Inequalities and Problem Solving

2. The Addition & Multiplication Properties of Equality
Section
2.2
The Addition & Multiplication Properties of Equality

3. Defining Linear Equations and Using the Addition Property
Objective 1
Defining Linear Equations and Using the Addition Property

4. Linear Equations An equation is of the form “expression = expression.”
An equation contains an equal sign and an expression does not.
Equations Expressions
Objective A

5. Linear Equations Linear Equation in One Variable
A linear equation in one variable can be written in the form
ax + b = c
where a, b, and c are real numbers and a ≠ 0.

6. Using the Addition Property to Solve Equations
Addition Property of Equality
Let a, b, and c represent numbers. Then
a = b and a + c = b + c
are equivalent equations.
Objective A

7. Example
Solve x – 4 = 7 for x.
Check:
Objective A

8. Example
Solve: y – 1.2 = –3.2 – 6.6
Objective A

9. Example
Solve:
Objective A

10. Example
Solve: 6x + 8 – 5x = 8 – 3
x + 8 – 8 = 5 – 8
Objective A

11. Example
Solve: 3(3x – 5) = 10x
Objective A

12. Example Solve: 4p – 11 – p = 2 + 2p – 20
3p – 11 = 2p – Simplify both sides.
3p + (– 2p) – 11 = 2p + (– 2p) – 18 Add –2p to both sides.
p – 11 = – Simplify both sides.
p – = – Add 11 to both sides.
p = – Simplify both sides.

13. Example Solve: 5(3 + z) – (8z + 9) = – 4z
15 + 5z – 8z – 9 = – 4z Use distributive property.
6 – 3z = – 4z Simplify left side.
6 – 3z + 4z = – 4z + 4z Add 4z to both sides.
6 + z = Simplify both sides.
6 + (–6) + z = 0 + (–6) Add –6 to both sides.
z = – Simplify both sides.

14. Using the Multiplication Property
Objective
Using the Multiplication Property

15. Example
Solve:
Objective A

16. Example
Solve –4x = 16 for x.
Check:
Objective A

17. Example
Solve: –1.2x = –36
Objective A

18. Example
Solve:
Multiply both sides by 7.
Simplify both sides.

19. Using Both the Addition and Multiplication Properties
Objective 3
Using Both the Addition and Multiplication Properties

20. Example
Solve: 4x – 8x = 16
Objective A

21. Example Solve: 3z – 1 = 26 3z – 1 = 26 3z – 1 + 1 = 26 + 1 3z = 27

22. Example Solve: 12x + 30 + 8x – 6 = 10 20x + 24 = 10

23. Example Solve: 5(2x + 3) = –1 + 7 5(2x) + 5(3) = –1 + 7 10x + 15 = 6

24. Writing Word Phrases as Algebraic Expressions
Objective 4
Writing Word Phrases as Algebraic Expressions

25. Example If x is the first two consecutive integers, express the
sum of the two integers in terms of x. Simplify if
possible.
The second consecutive integer is always 1 more than the first. If x is the first of two consecutive integers, the two consecutive integers are x and x + 1.
x + (x + 1) = 2x + 1

26. Example (cont) If x is the first two consecutive odd integers,
express the sum of the two integers in terms of x.
Simplify if possible.
The second consecutive odd integer is always 2 more than the first. If x is the first of two consecutive odd integers, the two consecutive integers are x and x + 2.
x + (x + 2) = 2x + 2